Exponents and Logarithms Exam Questions
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1 Eponents nd Logrithms Em Questions Nme: ANSWERS
2
3 Multiple Choice 1. If 4, then is equl to:. 5 b. 8 c. 16 d.. Identify the vlue of the -intercept of the function ln y.. -1 b. 0 c. d.. Which eqution is represented by the grph sketched below.. b. 1 y 1 y c. y d. y
4 4. The grph of 6 y intersects the grph of y 4 t:. 1 b. 1 c. 5 d The grph of 1 y compred to the grph of 1 y is :. reflection in the -is b. reflection in the y -is c. reflection in the line y d. reciprocl function 6. The grph of the function f shown below is best described by the eqution:. f b. f c. f d. f 4
5 7. Which of the following is resonble estimte for the vlue of 50?. b..5 c..8 d. 8. Solve: e ln b. ln c. ln7 ln5 d Simplify the following epression: 6. b. 4 c. 9 d Which of the following is closest to the vlue of ?. b. 8 c. 10 d. 45 5
6 11. The - intercept of the grph of y 1is:. -1 b. 0 c. 1 d The epression y s single rithm is:. y b. c. y y d. y 1. Determine the vlue of b. 1 c. d. 14. Identify n equivlent epression for b. 7 c. 10 d. 11 6
7 15. Solve: b. c. 7 d Identify the rithmic form of b. 5 6 c. 6 5 d
8 Written Response 17. Given, give one emple of possible vlues of nd b tht mke this eqution true. b (1 mrk) 18. Frnk tried to epnd rithmic epression using the lws of rithms. He mde one error. Frnk s solution: Write the correct solution. zw z w (1 mrk) 19. Estimte the vlue of 5 5. Justify your nswer. (1 mrk) 8
9 0. Clire correctly solves the following eqution: 6. She finds two possible vlues of : nd 7. Identify which one of these vlues is uncceptble nd eplin why. (1 mrk) 1. Which epression hs lrger vlue? 6 or 80 Justify your nswer. (1 mrk). Which of the following equtions could be solved without the use of rithms? Without ctully solving the problem, eplin your choice. (1 mrk) or
10 . Using the lws of rithms, epnd: ( mrks) y z 4. Determine the intercept nd intercept y of y 41. ( mrks) 5. Solve the following equtions lgebriclly: ( mrks)
11 6.. Sketch the grph of y. ( mrks) b. Eplin how the grph of y cn be used to sketch the grph of. y (1 mrk) 11
12 7. Determine the vlue of y in the following eqution: ( mrks) 7 y 8. The number of times website is visited cn be modeled by the function: e rt A 800 where A = the totl number of visitors t time t t = the time in dys t 0 r = the rte of growth After 5 dys, people hve visited the site. Determine the number of visitors epected fter 9 dys. Epress your nswer s whole number. (clcultor) ( mrks) 1
13 9.. Sketch the grph of y ln. ( mrks) b. Sketch the grph of ln y. ( mrks) 1
14 0. Solve lgebriclly: (clcultor) ( mrks) Jess invests $1 000 t rte of 4.75% compounded monthly. How long will it tke for Jess to triple her investment? Epress your nswer in yers, correct to deciml plces. (clcultor) ( mrks) 14
15 . Solve the following eqution: (4 mrks) An erthquke in Vncouver hd mgnitude of 6. on the Richter scle. An erthquke in Jpn hd mgnitude of 8.9 on the Richter scle. How mny times more intense ws the Jpn erthquke thn the Vncouver erthquke? You my use the formul below: A M A 0 where M is the mgnitude of the erthquke on the Richter scle A is the intensity of the erthquke A is the intensity of stndrd erthquke 0 Epress your nswer s whole number. (clcultor) ( mrks) 15
16 4.. Sketch the grph of 1 f. ( mrks) 1 b. Sketch the grph of f. (1 mrk) 16
17 5. Given nd , find the vlue of 1. ( mrks) (clcultor) 6. Solve the following eqution: (4 mrks)
18 7. Determine how mny monthly investments of $50 would hve to be deposited into svings ccount tht pys % nnul interest, compounded monthly, for the ccount s future vlue to be $50,000. R 1 i 1 Use the formul: FV i where: FV = the future vlue R = the investment mount the nnul interest rte i the number of compounding periods per yer n = the number of investments n Epress your nswer s whole number. (clcultor) ( mrks) 18
19 8. A popultion of 500 bcteri will triple in 0 hours. (clcultor) Using the formul given below, rt A Pe A = popultion fter t hours P = initil popultion r = rte of growth t = time in hours. Determine the rte of growth r. ( mrks) b. Determine how mny hours it will tke for the initil popultion to double with the sme rte of growth. ( mrks) 19
20 9. Sketch the grphs of: 1. y 4 ( mrks) b. 1 y (1 mrk) 4 0
21 40. Evlute: ( mrks) Solve the following eqution: ( mrks)
22 4. Identify which of these vlues is greter. Justify your nswer. (1 mrk) Solve: 5 5 (clcultor) (4 mrks)
23 44. A lke ffected by cid rin hs ph of 4.4. A person suffering from hertburn hs stomch cid of ph of 1.. The ph of solution is defined s ph -H where H is the hydrogen ion concentrtion. How mny times greter is the hydrogen ion concentrtion of the stomch thn tht of the lke? Epress your nswer s whole number. (clcultor) ( mrks) 45. Solve: (4 mrks)
24 46.. Sketch the grph of 5 1 f. ( mrks) 1 b. Sketch the grph of f. (1 mrk) 4
25 47. Kim solved the following rithmic eqution: Eplin why is n etrneous root. (1 mrk) Solve: 6 5 (clcultor) (4 mrks) Solution:
26 49. Evlute: 4 (1 mrk) Solution: Estimte the vlue of 5. Justify your nswer. (1 mrk) Solution: 4 8 therefore Sketch the grph of 1 f. ( mrks) 6
27 1 5. Solve: 4 8 ( mrks) Solution: Use the lw of rithms, fully epnd the epression: ( mrks) y z Solution: 1 y z y z 1 y z 54. Given 1 f, stte the eqution of the horizontl symptote. (1 mrk) Solution: y 1 7
28 55. Sheev s bnk is lending her $ t n nnul interest rte of 6%, compounded monthly, to purchse cr. Given tht the lst pyment will be prtil pyment, determine how mny full monthly pyments of $800 Sheev will hve to mke. The formul below my be used. R1 PV 1 i i n where PV = the present vlue of the mount borrowed R = the mount of ech periodic pyment nnul interest rte (s deciml) i the number of compounding periods per yer n = the number of equl periodic pyments. Epress your nswer s whole number. ( mrks) 8
29 56. Using the lws of rithms, fully epnd the epression: ( mrks) w 1 y 57. Solve the following eqution: ( mrks) 5 9
30 58. Solve: ( mrks) 59. Epnd using the lws of rithms. ( mrks) b 4 0
31 60. Peter invests $560 per month t n nnul interest rte of 4.%, compounded monthly. Determine how mny monthly investments he will need to mke to obtin t lest $ Epress your nswer s whole number. (clcultor) ( mrks) Use the formul: n R1 i 1 FV i where FV = the future vlue R = the investment mount ech period the nnul mount ech period i the number of compounding periods per yer n = the number of investments 1
32 61. Solve the following eqution lgebriclly: ( mrks) Justify why 4.7 is better estimte thn 4. for the vlue of 6. (1 mrk)
33 6. Sketch the grph of y. ( mrks) 64. Eplin why the domin of 1 y is 1. (1 mrk)
34 65. If 6 p, 5 r nd q, epress 60 in terms of p, q, nd r. ( mrks) 4
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